1. Field of the Invention
The invention relates to micromachined gyroscopes and in particular to two-mass angle measuring gyroscopes.
2. Description of the Prior Art
All non-micromachined angle measuring gyroscopes are expensive due to the necessity of precision machining to produce each individual device. Previous micromachined implementations of angle measuring gyroscopes used either a single shell or single proof mass as a drive and sense element. These implementations require nonlinear electrostatic actuation, which greatly complicate control, sense, and error suppression.
All micromachined rate gyroscopes are also vibratory in nature, measuring angular rates by detecting energy coupled between orthogonal vibration modes due to Coriolis force. A structural mass is forced into oscillation in one principle structural mode, designated the “drive” mode. The presence of a rotation induced Coriolis force couples the sustained oscillation into an orthogonal structural mode, designated the “sense” mode. The magnitude of vibration induced in the sense mode is proportional to the rotation rate of the device. An example is shown in U.S. Pat. No. 6,481,285, incorporated herein by reference.
As an illustration, consider a structural mass attached to a frame free to move in inertial space (i,j) as schematically shown in FIG. 1. In the coordinate frame of the moving device (X,Y), the equations of motion, assuming the operating frequency is much greater than the rotation rate       (                            Ω          2                ⁢                  <<                                    k              x                        m                              ,                        k          y                m              )    ,arem{umlaut over (x)}+kxx−2mΩ{dot over (y)}=Fd(t)  (1)mÿ+kyy+2mΩ{dot over (x)}=0  (2)where m is the lumped mass of the system, kx and ky are the x and y stiffness values, respectively, and Ω is an input angular rate. To achieve highest sensitivity, the stiffnesses between x and y are typically designed to be the same (kx=ky=k) and in this case, the system is driven at its resonant frequency using a harmonic excitation force Fd (Fd=F0 sin ωt, and ω=√(k/m). The measured sense acceleration ac is proportional to the input angular velocityac˜Ω.X0ωn cos ωt  (3)where X0 is the magnitude of vibration in the x direction. However, no micromachined rate gyroscope has been successful as a long term navigation grade sensor due to amplification of errors that arise from the necessity of integrating the angular rate signal to obtain attitude.